Beach, James W.||Christiano, John G.
M.S. (Master of Science)
Department of Mathematics
The application of Newton's Method to determine the approximate solution to an equation will, depending upon the equation and first approximation used, lead to an approximation which is equal to the first. If "a" is the root of the equation f(x)=0 and the approximation to this root is taken as a value x₁ which satisfies the equation (f(x₁))/(f'(x₁)) = 2(x₁-a), then the approximations to the root x=a will not get successively better, but will repeat themselves. Several cases in which this phenomenon occurs are discussed.
Duncker, William L., "Equal approximations in the Newton-Raphson method" (1967). Graduate Research Theses & Dissertations. 2895.
ii, 19 pages
Northern Illinois University
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.